On the second order derivatives of convex functions on the Heisenberg group
| dc.creator | Gutierrez, Cristian E. | |
| dc.creator | Montanari, Annamaria | |
| dc.date | 2003-09-09 | |
| dc.date.accessioned | 2026-07-07T05:00:59Z | |
| dc.date.available | 2026-07-07T05:00:59Z | |
| dc.description | In the Euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem states that convex functions are a.e. twice differentiable. In this paper we prove that a similar result holds in the Heisenberg group, by showing that every continuous H-convex function belongs to the class of functions whose second order horizontal distributional derivatives are Radon measures. Together with a recent result by Ambrosio and Magnani, this proves the existence a.e. of second order horizontal derivatives for the class of continuous H-convex functions in the Heisenberg group. | |
| dc.identifier | https://arxiv.org/abs/math/0309167 | |
| dc.identifier | http://arxiv.org/abs/math/0309167 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68523 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35B50; 35B45; 35H20 | |
| dc.title | On the second order derivatives of convex functions on the Heisenberg group | |
| dc.type | text |